Heaps and unpointed stable homotopy theory

Lukáš Vokřínek

Address: Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, CZ 611 37 Brno, Czech Republic

E-mail: koren@math.muni.cz

Abstract: In this paper, we show how certain “stability phenomena” in unpointed model categories provide the sets of homotopy classes with a canonical structure of an abelian heap, i.e. an abelian group without a choice of a zero. In contrast with the classical situation of stable (pointed) model categories, these sets can be empty.

AMSclassification: primary 55U35; secondary 55P42.

Keywords: stable homotopy, equivariant, fibrewise.

DOI: 10.5817/AM2014-5-323